When will the two trains collide?

[Rebecca Berger]

Homework Statement

Two trains approach each other on a straight level track: one from the east and the other from the west. Initially they are 7,500 meters apart and have a spray of 10meters/s with respect to the ground. If both locomotives accelerate toward the east at a constant rate of .025 meters/s^2, in how many minutes will they collide?

Homework Equations

X=X0+V0t+1/2at^2
V=V0+at
V^2=V0^2+2a(X-X0)

The Attempt at a Solution

For our class we're only allowed to use these equations. At dust I thought it would be simple to just find X but I forgot we weren't given final velocity. I'm missing v,x, and t. I tried plugging the numbers into the last equation to find X, but I just got v=10m/s +2(.025m/s)(X-0) or for the other train v=10m/s +2(.025m/s)(X-7500) I always end up with two missing parts. I might be over looking something, or have been spending too much time on homework and just need to sleep it out. Please let me know if I'm missing something! Thank you so much.

 

[Rebecca Berger]

I meant a speed of 10m/s, sorry

 

[SammyS]

Homework Statement

Two trains approach each other on a straight level track: one from the east and the other from the west. Initially they are 7,500 meters apart and have a spray of 10meters/s with respect to the ground. If both locomotives accelerate toward the east at a constant rate of .025 meters/s^2, in how many minutes will they collide?

Homework Equations

X=X0+V0t+1/2at^2
V=V0+at
V^2=V0^2+2a(X-X0)

The Attempt at a Solution

For our class we're only allowed to use these equations. At dust I thought it would be simple to just find X but I forgot we weren't given final velocity. I'm missing v,x, and t. I tried plugging the numbers into the last equation to find X, but I just got v=10m/s +2(.025m/s)(X-0) or for the other train v=10m/s +2(.025m/s)(X-7500) I always end up with two missing parts. I might be over looking something, or have been spending too much time on homework and just need to sleep it out. Please let me know if I'm missing something! Thank you so much.

I don't see how using that equation will help you. It doesn't have time in it, and you don't have any direct information about how the velocities are related except at t = 0. Also, you did not square the velocities.

You should use a different symbol for velocity of each train.

Isn't it true that v₀ is different for each train? Are they going the same direction initially?

 

[Rebecca Berger]

I don't see how using that equation will help you. It doesn't have time in it, and you don't have any direct information about how the velocities are related except at t = 0. Also, you did not square the velocities.

You should use a different symbol for velocity of each train.

Isn't it true that v₀ is different for each train? Are they going the same direction initially?

I asked my physics professor that question, he said they're going different directions but one is slowing down but the other is speeding up, but they both start at 10m/s, I would have thought one would be going a negative velocity. But what you're saying is that I do use the second equation, but I just plugged in the numbers wrong?

 

[SammyS]

I asked my physics professor that question, he said they're going different directions but one is slowing down but the other is speeding up, but they both start at 10m/s, I would have thought one would be going a negative velocity. But what you're saying is that I do use the second equation, but I just plugged in the numbers wrong?

I would not use the second equation either.

Yes, one velocity should be negative.